http://velonews.competitor.com/2013/11/bikes-and-tech/technical-faq/technical-faq-bifurcation-and-high-speed-shimmy_309601

There are many types of bifurcations, and they explain all sorts
of critical phenomena on nature, and this type, the Hopf bifurcation, explains
the onset of oscillations in all sorts of natural systems, from population
dynamics, to chemical reactions, to airplane wing flutter, to stability of
steerers in bicycles, trucks on trains (leading to derailment) to landing gear
wobble on airplanes.

To many engineers not in the know, these oscillations and their onset are often
mistaken for resonance, but it requires a nonlinearity in a certain way. This is
often guessed by the critical onset of the phenomena as a parameter is adjusted.

I am including some video of the flutter phenomenon which is an aero elasticity
phenomenon — airplane wings oscillate — you have probably seen it out of your
window of your last plane ride (hopefully if an airplane hits a bump in the air,
the wing oscillates back to its stable loaded state). But if the airplane goes
faster, this state becomes progressively unstable. At a critical speed, the
equilibrium becomes unstable, and there is born a limit cycle, which is a state
where the airplane wings oscillates at a fixed amplitude. But the amplitude
increases with increasing speed. Each airplane has a critical speed marked on
its airspeed indicator (called VNE standing for “Velocity Not Exceed”). I have
read that the FAA marks this fastest “safe” speed as 30 percent lower than the
actual critical Hopf instability speed to build in a margin of safety. Often the
wings fall off if you go Hopf. That’s bad.

http://youtu.be/iTFZNrTYp3k

http://youtu.be/kQI3AWpTWhM